Critical Wess-Zumino models with four supercharges from the functional renormalization group

Abstract

We analyze the $\mathcal{N}=1$ supersymmetric Wess-Zumino model dimensionally reduced to the $\mathcal{N}=2$ supersymmetric model in three Euclidean dimensions. As in the original model in four dimensions and the $\mathcal{N}=(2,2)$ model in two dimensions the superpotential is not renormalized. This property puts severe constraints on the non-trivial fixed-point solutions, which are studied in detail. We admit a field-dependent wave function renormalization that in a geometric language relates to a Kähler metric. The Kähler metric is not protected by supersymmetry and we calculate its explicit form at the fixed point. In addition we determine the exact quantum dimension of the chiral superfield and several critical exponents of interest, including the correction-to-scaling exponent $\omega$, within the functional renormalization group approach. We compare the results obtained at different levels of truncation, exploring also a momentum-dependent wave function renormalization. Finally we briefly describe a tower of multicritical models in continuous dimensions.

16 pages, 3 figures

References in corpus (24)

• Exact evolution equation for the effective potential
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Emergence of supersymmetry at a critical point of a lattice model
• Asymptotic safety: a simple example
• Ising exponents from the functional renormalisation group
• Critical behavior of the (2+1)-dimensional Thirring model
• Fermion-induced quantum criticality in two-dimensional Dirac semimetals: Non-perturbative flow equations, fixed points and critical exponents
• Multi-meson Yukawa interactions at criticality
• Bootstrapping Mixed Correlators in 4D $\mathcal{N}=1$ SCFTs
• Functional perturbative RG and CFT data in the $\epsilon$-expansion
• Fixed points and the spontaneous breaking of scale invariance
• Flow Equation for Supersymmetric Quantum Mechanics
• Phase Diagram and Fixed-Point Structure of two dimensional N=1 Wess-Zumino Models
• A functional perspective on emergent supersymmetry
• Asymptotically free scaling solutions in nonabelian Higgs models
• Convergence of Derivative Expansion in Supersymmetric Functional RG Flows
• Nonabelian Higgs models: paving the way for asymptotic freedom
• Products of composite operators in the exact renormalization group formalism
• The one-loop effective potential of the Wess-Zumino model revisited
• Nonperturbative renormalization-group approach preserving the momentum dependence of correlation functions
• Functional RG flow equation: regularization and coarse-graining in phase space
• Phase structure of a three-dimensional Yukawa model
• The two dimensional N=(2,2) Wess-Zumino Model in the Functional Renormalization Group Approach

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